How to "widen" a mesh modeling from scratch
Specifically addressing how to take a 'uniform grid' area of mesh and insert a new face loop ending in a single 'diamond' quad:

Select the series of vertices desired 'above' the 'diamond' location using Shift-clicks. Use Ctrl-B to bevel the selected edge loop, resulting in a triangle at the bottom. Then use Ctrl-R to loop cut down the centre of the newly created faces, such that you now have 2 new face loops running down into the 'diamond'.



This is still a "manual" process, and does need to be repeated every time one would want to perform this action, so I'm not sure if this answers the question, as the question doesn't specify how 'automatic' or how much of a short-cut is desired.

To take it further, it would be relatively straightforward to make an addon that performs these steps as a single operator, but I'm unaware if this has been done. It's somewhat subjective whether the default actions are fine- or coarse-grained enough for specific use cases, and when modelling one might very likely want to adjust the results at this fine-grained a level anyway.